A patrol officer pulled over the car after the driver cut him off on Monterey Road near San Pedro Avenue, Morgan Hill police Sgt. Jerry Neumayer said.
The driver, 40-year-old Ciro Paredes of Morgan Hill, did not have a driver's license, and the officer smelled alcohol in the vehicle, according to Neumayer.
During a search of the car, the patrol officer found open beer cans and plastic bags filled with what he suspected was crystal methamphetamine, Neumayer said.
The patrol officer reported that he heard what he thought was a crying baby coming from the trunk of the car, according to Neumayer.
The officer looked in the trunk and found a goat that had been hog-tied. The animal was malnourished but alive, Neumayer said.
Police called in an animal control officer, and the goat was transported to an animal shelter in San Martin, Neumayer said.
Paredes was arrested on suspicion of animal cruelty, DUI and driving with open alcohol containers.
Passengers Julio Perez, 27, and Ricardo Melgar, 19, were also arrested for animal cruelty, and Perez was arrested for possession of a controlled substance, according to Neumayer.
All three men were booked into Santa Clara County Jail, Neumayer said.